Based on the comments from the OP the real question is "What is an efficient algorithm to demodulate a DSB-SC signal." The FFT is not an efficient approach for this. A straight forward approach to demodulate a DSB-SC signal is to multiply the signal with the recovered carrier. Carrier recovery can be done by squaring the signal (frqeuency doubler), which will create a dominant tone at twice the carrier frequency which can then be divided by two.  Another approach is the Costas Loop as shown in the diagram below, which can be completely implemented digitally.  The loop will lock such that $cos(\epsilon) = 1$ recovering the modulation signal $A_m$. 

[![Costas Loop][1]][1]




  [1]: https://i.sstatic.net/hc3Yg.png